Question

show that 1÷(3_√8)-1÷(√8-√7)+1÷(√7-√6)-1(√6-√5)+1(√5-2)=5​

Answer 1

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We should show,

$\frac{1}{3-\sqrt{8} } -\frac{1}{\sqrt{8}-\sqrt{7} } -\frac{1}{\sqrt{7}-\sqrt{6} }-\frac{1}{\sqrt{6}-\sqrt{5} }-\frac{1}{\sqrt{5}-2 } =5$

Proof:-

First, We should rationalize all denominators:-

$\frac{1}{3-\sqrt{8} }\times\frac{3+\sqrt{8} }{3+\sqrt{8} } =3+\sqrt{8}$

$\frac{1}{\sqrt{8}-\sqrt{7} } \times \frac{\sqrt{8}+\sqrt{7} }{\sqrt{8}+\sqrt{7} }=\sqrt{8}+\sqrt{7}$

Similarly,

√7+√6

√6+√5

√5+2

So, now we should so,

3+√8-(√8-√7)-(√7-√6)-(√6-√5)-(√5-2)=5

3+√8-√8+√7-√7+√6-√6+√5-√5+2=5

3+2=5

5=5

LHS=RHS

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